[ { "path": ".gitattributes", "content": "* -text\n\n*.cs text eol=lf diff=csharp\n*.shader text eol=lf\n*.cginc text eol=lf\n*.hlsl text eol=lf\n*.compute text eol=lf\n\n*.meta text eol=lf\n" }, { "path": ".gitignore", "content": "Thumbs.db\nDesktop.ini\n.DS_Store\n*.swp\n\n/GeneratedAssets\n/Library\n/Logs\n/Recordings\n/Temp\n/UIElementsSchema\n/UserSettings\n\n/.utmp\n/mono_crash.*.json\n/Xcode\n/Web\n\n/*.app\n/*.exe\n/*.apk\n/*_DoNotShip\n/*.tgz\n\n" }, { "path": "Assets/BurstDft.cs", "content": "using System.Linq;\nusing Unity.Collections;\nusing Unity.Jobs;\nusing Unity.Mathematics;\n\n// Naive DFT vectorized/parallelized with the Burst compiler\n\npublic sealed class BurstDft : IDft, System.IDisposable\n{\n #region Public properties and methods\n\n public NativeArray Spectrum => _buffer;\n\n public BurstDft(int width)\n {\n // DFT coefficients\n var coeffs = Enumerable.Range(0, width / 2 * width).\n Select(i => (k: i / width, n: i % width)).\n Select(I => 2 * math.PI / width * I.k * I.n);\n\n var coeffs_r = coeffs.Select(x => math.cos(x));\n var coeffs_i = coeffs.Select(x => math.sin(x));\n\n _coeffs_r = PersistentMemory.New(coeffs_r);\n _coeffs_i = PersistentMemory.New(coeffs_i);\n\n // Output buffer\n _buffer = PersistentMemory.New(width / 2);\n }\n\n public void Dispose()\n {\n if (_coeffs_r.IsCreated) _coeffs_r.Dispose();\n if (_coeffs_i.IsCreated) _coeffs_i.Dispose();\n if (_buffer.IsCreated) _buffer.Dispose();\n }\n\n public void Transform(NativeArray input)\n {\n // Dispatch and complete the DFT jobs with the input.\n new DftJob \n { I = input.Reinterpret(4),\n Cr = _coeffs_r.Reinterpret(4),\n Ci = _coeffs_i.Reinterpret(4),\n O = _buffer }\n .Schedule(input.Length / 2, 1).Complete();\n }\n\n #endregion\n\n #region Private members\n\n NativeArray _coeffs_r;\n NativeArray _coeffs_i;\n NativeArray _buffer;\n\n #endregion\n\n #region DFT job\n\n [Unity.Burst.BurstCompile(CompileSynchronously = true)]\n struct DftJob : IJobParallelFor\n {\n [ReadOnly] public NativeArray I;\n [ReadOnly] public NativeArray Cr;\n [ReadOnly] public NativeArray Ci;\n [WriteOnly] public NativeArray O;\n\n public void Execute(int i)\n {\n var N = I.Length;\n var offs = i * N;\n\n var rl = 0.0f;\n var im = 0.0f;\n\n for (var n = 0; n < N; n++)\n {\n var x = I[n];\n rl += math.dot(x, Cr[offs + n]);\n im -= math.dot(x, Ci[offs + n]);\n }\n\n O[i] = math.sqrt(rl * rl + im * im) * 0.5f / N;\n }\n }\n\n #endregion\n}\n" }, { "path": "Assets/BurstDft.cs.meta", "content": "fileFormatVersion: 2\nguid: f23422a3c09909e41957e32264e9bc58\nMonoImporter:\n externalObjects: {}\n serializedVersion: 2\n defaultReferences: []\n executionOrder: 0\n icon: {instanceID: 0}\n userData: \n assetBundleName: \n assetBundleVariant: \n" }, { "path": "Assets/BurstFft.cs", "content": "#define SINGLE_THREAD\n\nusing System.Linq;\nusing Unity.Collections;\nusing Unity.Mathematics;\nusing Unity.Jobs;\n\n// Cooley–Tukey FFT vectorized/parallelized with the Burst compiler\n\npublic sealed class BurstFft : IDft, System.IDisposable\n{\n #region Public properties and methods\n\n public NativeArray Spectrum => _O;\n\n public BurstFft(int width)\n {\n _N = width;\n _logN = (int)math.log2(width);\n\n BuildPermutationTable();\n BuildTwiddleFactors();\n\n _O = PersistentMemory.New(_N);\n }\n\n public void Dispose()\n {\n if (_P.IsCreated) _P.Dispose();\n if (_T.IsCreated) _T.Dispose();\n if (_O.IsCreated) _O.Dispose();\n }\n\n #if SINGLE_THREAD\n\n public void Transform(NativeArray input)\n {\n var X = TempJobMemory.New(_N / 2);\n\n // Bit-reversal permutation and first DFT pass\n new FirstPassJob { I = input, P = _P, X = X }.Run(_N / 2);\n\n // 2nd and later DFT passes\n for (var i = 0; i < _logN - 1; i++)\n {\n var T_slice = new NativeSlice(_T, _N / 4 * i);\n new DftPassJob { T = T_slice, X = X }.Run(_N / 4);\n }\n\n // Postprocess (power spectrum calculation)\n var O2 = _O.Reinterpret(sizeof(float));\n new PostprocessJob { X = X, O = O2, s = 2.0f / _N }.Run(_N / 2);\n\n X.Dispose();\n }\n\n #else\n\n public void Transform(NativeArray input)\n {\n var X = TempJobMemory.New(_N / 2);\n\n // Bit-reversal permutation and first DFT pass\n var handle = new FirstPassJob { I = input, P = _P, X = X }\n .Schedule(_N / 2, 32);\n\n // 2nd and later DFT passes\n for (var i = 0; i < _logN - 1; i++)\n {\n var T_slice = new NativeSlice(_T, _N / 4 * i);\n handle = new DftPassJob { T = T_slice, X = X }\n .Schedule(_N / 4, 32, handle);\n }\n\n // Postprocess (power spectrum calculation)\n var O2 = _O.Reinterpret(sizeof(float));\n handle = new PostprocessJob { X = X, O = O2, s = 2.0f / _N }\n .Schedule(_N / 2, 32, handle);\n\n handle.Complete();\n X.Dispose();\n }\n\n #endif\n\n #endregion\n\n #region Private members\n\n readonly int _N;\n readonly int _logN;\n NativeArray _O;\n\n #endregion\n\n #region Bit-reversal permutation table\n\n NativeArray _P;\n\n void BuildPermutationTable()\n {\n _P = PersistentMemory.New(_N / 2);\n for (var i = 0; i < _N; i += 2)\n _P[i / 2] = math.int2(Permutate(i), Permutate(i + 1));\n }\n\n int Permutate(int x)\n => Enumerable.Range(0, _logN)\n .Aggregate(0, (acc, i) => acc += ((x >> i) & 1) << (_logN - 1 - i));\n\n #endregion\n\n #region Precalculated twiddle factors\n\n struct TFactor\n {\n public int2 I;\n public float2 W;\n\n public int i1 => I.x;\n public int i2 => I.y;\n\n public float4 W4\n => math.float4(W.x, math.sqrt(1 - W.x * W.x),\n W.y, math.sqrt(1 - W.y * W.y));\n }\n\n NativeArray _T;\n\n void BuildTwiddleFactors()\n {\n _T = PersistentMemory.New((_logN - 1) * (_N / 4));\n\n var i = 0;\n for (var m = 4; m <= _N; m <<= 1)\n for (var k = 0; k < _N; k += m)\n for (var j = 0; j < m / 2; j += 2)\n _T[i++] = new TFactor\n { I = math.int2((k + j) / 2, (k + j + m / 2) / 2),\n W = math.cos(-2 * math.PI / m * math.float2(j, j + 1)) };\n }\n\n #endregion\n\n #region First pass job\n\n [Unity.Burst.BurstCompile(CompileSynchronously = true)]\n struct FirstPassJob : IJobParallelFor\n {\n [ReadOnly] public NativeArray I;\n [ReadOnly] public NativeArray P;\n [WriteOnly] public NativeArray X;\n\n public void Execute(int i)\n {\n var a1 = I[P[i].x];\n var a2 = I[P[i].y];\n X[i] = math.float4(a1 + a2, 0, a1 - a2, 0);\n }\n }\n\n #endregion\n\n #region DFT pass job\n\n [Unity.Burst.BurstCompile(CompileSynchronously = true)]\n struct DftPassJob : IJobParallelFor\n {\n [ReadOnly] public NativeSlice T;\n [NativeDisableParallelForRestriction] public NativeArray X;\n\n static float4 Mulc(float4 a, float4 b)\n => a.xxzz * b.xyzw + math.float4(-1, 1, -1, 1) * a.yyww * b.yxwz;\n\n public void Execute(int i)\n {\n var t = T[i];\n var e = X[t.i1];\n var o = Mulc(t.W4, X[t.i2]);\n X[t.i1] = e + o;\n X[t.i2] = e - o;\n }\n }\n\n #endregion\n\n #region Postprocess Job\n\n [Unity.Burst.BurstCompile(CompileSynchronously = true)]\n struct PostprocessJob : IJobParallelFor\n {\n [ReadOnly] public NativeArray X;\n [WriteOnly] public NativeArray O;\n public float s;\n\n public void Execute(int i)\n {\n var x = X[i];\n O[i] = math.float2(math.length(x.xy), math.length(x.zw)) * s;\n }\n }\n\n #endregion\n}\n" }, { "path": "Assets/BurstFft.cs.meta", "content": "fileFormatVersion: 2\nguid: 86b9e2bf2f83de24ba088ea221442def\nMonoImporter:\n externalObjects: {}\n serializedVersion: 2\n defaultReferences: []\n executionOrder: 0\n icon: {instanceID: 0}\n userData: \n assetBundleName: \n assetBundleVariant: \n" }, { "path": "Assets/IDft.cs", "content": "using Unity.Collections;\n\npublic interface IDft\n{\n NativeArray Spectrum { get; }\n void Transform(NativeArray input);\n}\n" }, { "path": "Assets/IDft.cs.meta", "content": "fileFormatVersion: 2\nguid: b1b0b515d575c044cb25d53ad2f0b689\nMonoImporter:\n externalObjects: {}\n serializedVersion: 2\n defaultReferences: []\n executionOrder: 0\n icon: {instanceID: 0}\n userData: \n assetBundleName: \n assetBundleVariant: \n" }, { "path": "Assets/NaiveDft.cs", "content": "using Unity.Collections;\nusing Unity.Mathematics;\n\n// Naive DFT implementation\n\npublic sealed class NaiveDft : IDft, System.IDisposable\n{\n public NativeArray Spectrum => _buffer;\n\n NativeArray _buffer;\n\n public NaiveDft(int width)\n => _buffer = PersistentMemory.New(width / 2);\n\n public void Dispose()\n {\n if (_buffer.IsCreated) _buffer.Dispose();\n }\n\n public void Transform(NativeArray input)\n {\n var N = _buffer.Length * 2;\n\n for (var k = 0; k < N / 2; k++)\n {\n var acc = float2.zero;\n\n for (var n = 0; n < N; n++)\n {\n var x = input[n];\n var t = 2 * math.PI / N * k * n;\n acc += math.float2(math.cos(t) * x, -math.sin(t) * x);\n }\n\n _buffer[k] = math.length(acc) * 2 / N;\n }\n }\n}\n" }, { "path": "Assets/NaiveDft.cs.meta", "content": "fileFormatVersion: 2\nguid: a659ccee364aad54284e1f2508c35acd\nMonoImporter:\n externalObjects: {}\n serializedVersion: 2\n defaultReferences: []\n executionOrder: 0\n icon: {instanceID: 0}\n userData: \n assetBundleName: \n assetBundleVariant: \n" }, { "path": "Assets/Test.cs", "content": "using System.Collections.Generic;\nusing System.Linq;\nusing UnityEngine;\nusing UnityEngine.UIElements;\nusing Unity.Collections;\nusing Unity.Mathematics;\nusing Stopwatch = System.Diagnostics.Stopwatch;\n\nsealed class Test : MonoBehaviour\n{\n const int Width = 1024;\n\n IEnumerable TestData\n => Enumerable.Range(0, Width)\n .Select(i => (float)i / Width)\n .Select(x => 5 * noise.snoise(math.float2(0.324f, x * 1000))\n + math.sin(x * 33)\n + math.sin(x * 300)\n + math.sin(x * 900));\n\n Texture2D Benchmark(TDft dft, NativeArray input)\n where TDft : IDft, System.IDisposable\n {\n var texture = new Texture2D(Width / 2, 1, TextureFormat.RFloat, false);\n\n // We reject the first test.\n dft.Transform(input);\n\n var sw = new System.Diagnostics.Stopwatch();\n\n // Benchmark\n const int iteration = 32;\n sw.Start();\n for (var i = 0; i < iteration; i++) dft.Transform(input);\n sw.Stop();\n\n // Show the average time.\n var us = 1000.0 * 1000 * sw.ElapsedTicks / Stopwatch.Frequency;\n 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assetBundleName: \n assetBundleVariant: \n" }, { "path": "Assets/Utils.cs", "content": "using System.Collections.Generic;\nusing System.Linq;\nusing Unity.Collections;\n\npublic static class TempJobMemory\n{\n public static NativeArray New(IEnumerable e) where T : unmanaged\n => new NativeArray(e.ToArray(), Allocator.TempJob);\n\n public static NativeArray New(int size) where T : unmanaged\n => new NativeArray(size, Allocator.TempJob,\n NativeArrayOptions.UninitializedMemory);\n}\n\npublic static class PersistentMemory\n{\n public static NativeArray New(IEnumerable e) where T : unmanaged\n => new NativeArray(e.ToArray(), Allocator.Persistent);\n\n public static NativeArray New(int size) where T : unmanaged\n => new NativeArray(size, Allocator.Persistent,\n NativeArrayOptions.UninitializedMemory);\n}\n" }, { "path": "Assets/Utils.cs.meta", "content": "fileFormatVersion: 2\nguid: 1c671880e86837e4bb90991259e16c21\nMonoImporter:\n externalObjects: {}\n serializedVersion: 2\n defaultReferences: []\n executionOrder: 0\n icon: {instanceID: 0}\n userData: \n assetBundleName: \n assetBundleVariant: \n" }, { "path": "LICENSE", "content": "This is free and unencumbered software released into the public domain.\n\nAnyone is free to copy, modify, publish, use, compile, sell, or\ndistribute this software, either in source code form or as a compiled\nbinary, for any purpose, commercial or non-commercial, and by any\nmeans.\n\nIn jurisdictions that recognize copyright laws, the author or authors\nof this software dedicate any and all copyright interest in the\nsoftware to the public domain. We make this dedication for the benefit\nof the public at large and to the detriment of our heirs and\nsuccessors. We intend this dedication to be an overt act of\nrelinquishment in perpetuity of all present and future rights to this\nsoftware under copyright law.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.\nIN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR\nOTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,\nARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR\nOTHER DEALINGS IN THE SOFTWARE.\n\nFor more information, please refer to \n" }, { "path": "Packages/manifest.json", "content": "{\n \"dependencies\": {\n \"com.unity.burst\": \"1.8.28\",\n \"com.unity.inputsystem\": \"1.18.0\",\n \"com.unity.mathematics\": \"1.3.3\",\n \"com.unity.modules.uielements\": \"1.0.0\"\n }\n}\n" }, { "path": "Packages/packages-lock.json", "content": "{\n \"dependencies\": {\n \"com.unity.burst\": {\n 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!u!890905787 &1\nVersionControlSettings:\n m_ObjectHideFlags: 0\n m_Mode: Visible Meta Files\n m_TrackPackagesOutsideProject: 0\n" }, { "path": "ProjectSettings/XRSettings.asset", "content": "{\n \"m_SettingKeys\": [\n \"VR Device Disabled\",\n \"VR Device User Alert\"\n ],\n \"m_SettingValues\": [\n \"False\",\n \"False\"\n ]\n}" }, { "path": "README.md", "content": "BurstFFT\n========\n\n**BurstFFT** is an FFT (Fast Fourier Transform) implementation in\nhigh-performance C# with Unity's Burst compiler.\n\nThis repository contains the following three variants of Fourier transform\nimplementation.\n\n- NaiveDFT: Unoptimized naive C# implementation of DFT\n- BurstDFT: Vectorized/parallelized DFT implementation, optimized with Burst\n- BurstFFT: Vectorized Cooley-Tukey FFT implementation, optimized with Burst\n\nYou can also enable parallelization on BurstFFT by disabling the `SINGLE_THREAD`\nsymbol in `BurstFft.cs`.\n\nResults\n-------\n\n### Windows Desktop (Ryzen 7 3700X, 3.6GHz, 8 cores)\n\n![table](https://i.imgur.com/yAr8hW6.png)\n\n![graph](https://i.imgur.com/1K5a3mR.png)\n\n### MacBook Pro 15 Late 2013 (Core i7, 2.3GHz, 4 cores)\n\n![table](https://i.imgur.com/bVoMbdP.png)\n\n![graph](https://i.imgur.com/CidTQKx.png)\n\nThoughts and Findings\n---------------------\n\n- It's quite easy to parallelize DFT with Unity's C# Job System. The more cores\n it has, the faster it runs.\n- Although the parallelized DFT runs quite fast compared to the unoptimized one,\n it never beat the single-threaded FFT.\n- The traditional Cooley-Tukey FFT is hard to parallelize in a performant way.\n The results above show that the 8-core BurstFFT runs slower than the 4-core\n one.\n" } ]